Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations

Details Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations

Aug 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007phpl...14h2701z&link_type=abstract

Physics of Plasmas, Volume 14, Issue 8, pp. 082701-082701-8 (2007).

Physics

10

Magnetohydrodynamics And Plasmas, Hydrodynamics, Laboratory Studies Of Space- And Astrophysical-Plasma Processes, Plasma Turbulence, Plasma Dynamics And Flow, Magnetohydrodynamic And Fluid Equation

Scientific paper

The Euler similarity criteria for laboratory experiments and time-dependent mixing transition are important concepts introduced recently for application to prediction and analysis of astrophysical phenomena. However, Euler scaling by itself provides no information on the distinctive spectral range of high Reynolds number turbulent flows found in astrophysics situations. On the other hand, time-dependent mixing transition gives no indication on whether a flow that just passed the mixing transition is sufficient to capture all of the significant dynamics of the complete astrophysical spectral range. In this paper, a new approach, based on additional insight gained from review of Navier-Stokes turbulence theory, is developed. It allows for revelations about the distinctive spectral scale dynamics associated with high Reynolds number astrophysical flows. From this perspective, the energy-containing range of the turbulent flow measured in a laboratory setting must not be unintentionally contaminated in such a way that the interactive influences of this spectral scale range in the corresponding astrophysical situation cannot be faithfully represented. In this paper, the concept of a minimum state is introduced as the lowest Reynolds number turbulent flow that a time-dependent mixing transition must achieve to fulfill this objective. Later in the paper, the Reynolds number of the minimum state is determined as 1.6×105. The temporal criterion for the minimum state is also obtained. The efforts here can be viewed as a unification and extension of the concepts of both similarity scaling and transient mixing transition concepts. Finally, the implications of our approach in planning future intensive laser experiments or massively parallel numerical simulations are discussed. A systematic procedure is outlined so that as the capabilities of the laser interaction experiments and supporting results from detailed numerical simulations performed in recently advanced supercomputing facilities increase progressively, a strategy is developed so that a progressively increasing range of dynamic structures and their statistical influences on evolving astrophysical flows can be attained in laboratory investigations.

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